# A Multiscale Study of Transformation Induced Plasticity (TRIP) in Quench and Partitioned (QP) Steels for Enhanced Ductility

With the rising need for higher fuel efficiency in vehicles, newer materials for structural components are being developed. Given that steel is the primary material utilized in automobile bodies, superior strength and ductility are required from newer grades of steels. One proposed steel grade for automotive applications is quenched and partitioned (QP) steel, which relies upon the transformation induced plasticity (TRIP) effect. The TRIP effect occurs when one lattice structure transforms into another when plastic strain is applied. In the case of QP steels with two phases, the TRIP effect involves the transformation of austenitic phase (face centered cubic- FCC) into martensitic phase (body centered cubic-BCC) during the application of strain. Increased TRIP behavior would result in to higher ductility, and correspondingly better formability in automotive components.

In order to fully harness the increased ductility due to TRIP, a thorough understanding of the TRIP effect must be established. To do so, an ICME approach is applied towards the steel, with the goal of downscaling the stress-strain response during forming, as well as predicting strength and stiffness of the formed part. The downscaling begins with crystal plasticity (CP) simulations at the polycrystalline level. Information required for CP simulations can be obtained from dislocation dynamics (DD) computations at lower length scales. In order to perform DD simulations, information about dislocation mobility must be obtained from atomistic scale simulations using methods such as the modified embedded atom method (MEAM). The parameters required to run MEAM can be obtained by running electronics level calculations such as density functional theory (DFT) for each of the lattice structures (FCC and BCC).

Moving onto upscaling, elastic moduli and stacking fault energies from the DFT calculations can now be fed back upscale. Subsequently, atomistic simulations can now define dislocation velocities, as well as their interactions near phase boundaries. The dislocation mobility thus obtained can be used to run DD simulations to establish hardening rules for the phases, as well as how multiple dislocations can pile up and interact at interphase boundaries. All the information then gets transferred to the CP level, where the micromechanical response of the material can be assessed using finite element methods.

Note that during plastic loading, the TRIP effect causes the underlying microstructure to change as a function of the plastic strain. To capture the evolving of the microstructure, information from the polycrystalline CP simulations is fed into a phase field model (PFM) which tracks the transformation of austenite (FCC) to martensite (BCC) over time. Information about the newly altered microstructure is then fed back to CP and the behavior during plastic loading is successively iterated. In addition to upscaling the polycrystalline response from the CP simulations, the PFM simulations can also upscale the stresses required for phase transformations (along with any potential volume changes during TRIP) up to the macroscale continuum level in the form of internal state variables (ISVs) that feed into the model. All the up scaled data at the continuum scale can then be used to predict the response of a formed automotive component, as well as optimize the processing and properties of the final part.

For better optimization, sources of uncertainty at each length scale must be recognized and factored into the multiscale modelling process. Uncertainty quantification will help establish bounds over expected properties and material responses from the optimized part. Furthermore, the uncertainty bounds during simulation can also serve as arbiters to compare against the bounds and tolerances available to the manufacturers of the actual part. Since the physical parameters of a production line often have certain bounds of error, a comparison against a well calibrated uncertainty quantification can help the engineers judge the feasibility of using the production lines to manufacture the given component while meeting all the design and safety requirements of the end product.